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Simplifying (x2) + -40x + -400 = 0 x2 + -40x + -400 = 0 Reorder the terms: -400 + -40x + x2 = 0 Solving -400 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + -40x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -40x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -40x + x2 = 0 + 400 -40x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -40x + x2 = 400 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 400 + 400 Reorder the terms: 400 + -40x + x2 = 400 + 400 Combine like terms: 400 + 400 = 800 400 + -40x + x2 = 800 Factor a perfect square on the left side: (x + -20)(x + -20) = 800 Calculate the square root of the right side: 28.284271247 Break this problem into two subproblems by setting (x + -20) equal to 28.284271247 and -28.284271247.Subproblem 1
x + -20 = 28.284271247 Simplifying x + -20 = 28.284271247 Reorder the terms: -20 + x = 28.284271247 Solving -20 + x = 28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 28.284271247 + 20 Combine like terms: -20 + 20 = 0 0 + x = 28.284271247 + 20 x = 28.284271247 + 20 Combine like terms: 28.284271247 + 20 = 48.284271247 x = 48.284271247 Simplifying x = 48.284271247Subproblem 2
x + -20 = -28.284271247 Simplifying x + -20 = -28.284271247 Reorder the terms: -20 + x = -28.284271247 Solving -20 + x = -28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -28.284271247 + 20 Combine like terms: -20 + 20 = 0 0 + x = -28.284271247 + 20 x = -28.284271247 + 20 Combine like terms: -28.284271247 + 20 = -8.284271247 x = -8.284271247 Simplifying x = -8.284271247Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.284271247, -8.284271247}
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